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Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial. (English) Zbl 0921.34032
The authors study the isochronous centers of two-dimensional autonomous systems in the plane $$\dot x= -y+X_s(x, y),\quad \dot y=x+Y_s(x,y),$$ where $X_s(x,y)$ and $Y_s (x,y$) are homogeneous polynomials of degree $s=4.$ A center is isochronous if the period of all integral curves in a neighborhood of the origin is constant. Necessary conditions for such isochronous center are obtained. Reversible systems that have an isochronous center at the origin are studied.

MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34A05Methods of solution of ODE
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References:
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